Rippon and Stallard discovered that the
fast escaping set \(\operatorname{A}(f)\) , which was
originally introduced by Bergweiler and Hinkkanen [1]},
shares many significant features with \(I(f)\) .
If we set \(M(f,r):=\max _{\left|z\right|=r}\left|f(z)\right|\)  and choose any constant \(R\)  such that
\(\operatorname{M}(f,r)>r\ \text{whenever} \ r\ge R,\) 
